The Israeli prime minister, Binyamin Netanyahu, used a visit to the White House on Monday to urge the US president to maintain or even increase sanctions against Iran, despite the promise of progress over Tehran's nuclear program.

"If diplomacy is to work, those pressures must be kept in place," Netanyahu said of the sanctions, which have proved economically crippling in Iran.

The two leaders met at the White House just days after Obama's historic 15-minute phone call with the new Iranian President Hassan Rouhani, which has been interpreted as a possile prelude to a thaw in relations between the US and Iran.

Israel has been sceptical of Rouhani's diplomatic overtures at the United Nations general assembly in New York last week. Netanyahu will deliver his own speech to the assembly on Tuesday.

Sitting next to Obama in the Oval Office, Netanyahu said: "Iran's conciliatory words have to be matched by real actions – transparent, verifiable, meaningful actions. Iran is committed to Israel's destruction."

He added: "Iran must fully dismantle its military nuclear program. If Iran continues to advance its military program during negotiations, the sanctions should be strengthened."

Obama reiterated the commitment of the US to Israel, one of its closest allies. "We enter into these negotiations very clear-eyed," Obama said, adding that Iranian words "are not sufficient".

The president said: "We have to have actions that give the international community confidence that in fact they are meeting their international obligations fully and they are not in a position to have a nuclear weapon.

"We have to test diplomacy. We have to see if in fact they are serious about their willingness to abide by international norms and international law and international requirements and resolutions."

The Israeli prime minister was scheduled to meet the US secretary of state John Kerry and, later on Monday, Republican and Democratic lawmakers on Capitol Hill.